**1. Introduction**

Opportunities to engage in early math learning is an equity issue with lasting consequences, as math learning *before* kindergarten entry strongly impacts and predicts future success in school [1]. All children deserve to be inspired by math and to reach their full potential, but for many, differences in math knowledge are evident at kindergarten entry, favoring children who have greater access to economic resources [2, 3]. This results in persistent educational learning gaps, as children who start kindergarten behind in mathematics may struggle to catch up to their peers [3, 4]. Addressing this challenge requires investing in early childhood programs and supporting families as education partners [5] as early intervention with preschoolers could help to narrow this gap and have important longer-term implications [6].

All children, no matter where they live, should have what they need to learn and develop well. Some children are born into communities where resources are abundant, but others may not be. In our work, we prioritize the communities that are under-resourced, so all families have the information they need to launch their children on a path to success. When children have opportunities to engage in meaningful mathematical interactions it can support their cognitive development and foster the skills and behaviors they need to engage in learning, such as problem-solving, puzzling, and persevering. The very skills they will need to successfully navigate life and work in the twenty-first century.

### **1.1 Importance of math learning**

Early mathematics knowledge is considered a critical component of young children's foundational cognitive skills [7] and the early years provide a pivotal opportunity to tap into children's curiosity and motivation to learn from interactions that are enriched with mathematics [8–10]. Accumulating research evidence indicates that children's early math knowledge predicts their future academic outcomes and success in school, [1, 11–13], on high stakes standards-based math tests in middle school [14], and through high school [15]. Importantly, early math skills predict later literacy skills [16] and are an even stronger predictor of later outcomes than early reading skills [1]. In fact, supporting kindergarteners' early mathematics skills builds a foundation not only for advanced mathematical knowledge but also for achievement in reading [17] and science and engineering [13, 18]. Indeed, knowing how to bolster children's mathematics learning at home and in classroom settings, through games and other developmentally appropriate activities, is of great interest to families, educators, early childhood leaders, and policymakers [19].
